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1
Content available remote Road to chaos in a Duflng oscillator with time delay loop
Borkowski Łukasz
Mechanics and Mechanical Engineering
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2021
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Vol. 25, nr 1
84--87
EN
This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.
2
Content available remote Criterion for transient behaviour in a nonlinear Duffing oscillator
Szczebiot Ryszard, Jordan Andrzej
Przegląd Elektrotechniczny
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2019
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R. 95, nr 4
196--199
EN
The paper proposes a criterion for determining transient behaviour in a nonlinear Duffing oscillator. For this purpose studies of specific attractors typical of the system have been conducted. Exactly defined deviation value of ∆ with respect to the mean value of the surface areas bounded by the successive trajectory cycles has been assumed as the termination of the transient behaviour.
PL
W pracy zaproponowano kryterium wyznaczania czasu trwania procesu przejściowego w nieliniowym oscylatorze Duffinga. W tym celu badano specyficzne atraktory charakteryzujące ten układ. Za kryterium końca procesu przejściowego przyjęto ściśle zdefiniowaną wartość odchyłki ∆ od wartości średniej pól powierzchni ograniczonych kolejnymi cyklami trajektorii.
3
Content available remote Prediction of solutions of the Duffing system with tuned mass damper
Mnich K.
Mechanics and Mechanical Engineering
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2018
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Vol. 22, nr 4
983--989
EN
In this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffng oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.
4
Content available Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
Kabziński J.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 4
625--634
EN
The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.
5
Content available The dynamics of the cutting process with Duffing nonlinearity
Weremczuk A., Kęcik K., Rusinek R., Warmiński J.
Eksploatacja i Niezawodność
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2013
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Vol. 15, no. 3
209-213
EN
The paper presents the nonlinear one degree of freedom model of cutting process. To describe the dynamics the Duffing model with time delay part is used. The model is solved analytically by using the multiple time scale method. The stability lobe diagrams are determined numerically and analytically. The obtained results show that stability region depends on initial conditions of the system.
PL
W artykule przedstawiono jednowymiarowy nieliniowy model skrawania. Do opisu procesu przyjęto model Duffinga z opóźnieniem czasowym. Model rozwiązano analitycznie za pomocą metody wielu skal czasowych. Wykres stabilności otrzymano numerycznie i analitycznie. Wykazano, że obszary stabilności zależą od warunków początkowych układu.
6
Chaotic behavior description in technical systems
Houfek L., Kratochvil C., Krejsa J., Houfek M., Navrat Τ.
Modelling and Optimization of Physical Systems
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2007
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z. 6
77--80
EN
Chaotic behavior of technical systems is lately under great interest of researchers. The paper describes a possibility to analyze system which exhibits chaotic oscillations. For simplicity the model of Duffing oscillator was selected as analyzed case, as the chaotic oscillations occur in this model. Bifurcation diagram and phase plane analysis are used as analysis tool.
7
Content available remote Dynamics of an Array of Duffing Oscillators Suspended on Elastic Etructures
Czołczyński K., Stefański A., Perlikowski P., Kapitaniak T.
Machine Dynamics Problems
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2007
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Vol. 31, No. 2
57-65
EN
We consider the dynamics of externally excited chaotic oscillators suspended on the elastic structure. We show that for the given conditions of oscillations of the structure, initially uncorrelated chaotic oscillators become periodic and synchronous. In the periodic regime we observed synchronized clusters and multistability as different attractors coexist.
8
Content available remote Synchronization of coupled mechanical oscillators
Perlikowski P., Stefański A.
Mechanics and Mechanical Engineering
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2006
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Vol. 10, nr 1
110-116
EN
Complete synchronization of coupled chaotic systems is usually a primary and crucial issue. Coupling in mechanical systems introduces mutual perturbation of their dynamics. In case of identical systems such perturbation can lead to the synchronization. We can predict the synchronization threshold of such systems using a concept called Master Stability Function (MSF). As a tool of MSF we use transverse Lyapunov exponents, which characterize the stability of synchronization state. We show areas of synchronization in coupling parameters space in typical nonlinear systems: Duffing and Duffing - Van der Pol oscillators.
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